238 THE REV. ROBERT HARLEY ON A CERTAIN CLASS 



H- 60(3 1 + 1 73^?^ + 46.27^)^y 

 + 30(121 + 328,27^ + 5 ia?^)<2?'y^ 



+ 3(77 + 22I4<2?^+ 2541.3?^ + l68<27")y 

 — 300(17+ 134^ + 49<27^)<2?}. 



And combining as before^, so as to eliminate all powers of 

 y higher than the firsts we find 



the differential resolvent for the quintic. 



6. If now we collect these several resolvents and apply 

 to them Dr. Boole's process for passing from the ordinary 

 to the symbolical form of a differential equation^ we find 

 that 



For the quadratic, the resolvent is 



Dy-(D-2y2,=V 



For the cubic, it is 



D(D-i)2/-(D-|)(D-p6'*2^=o, 

 or, which is the same thing, 



[D]>-(|)^[^5]>,=o. 



For the biquadratic, it is 



D(D-i)(D-2)2,-(D-0(D-^)(D-^)e"2/ = o, 

 or, what is the same thing, 



[D]',-(2)'[to]'e., = o. 



